QUESTION

(a) (i) Explain the following terms in relation to linear programming problems-

(1) decision variables

(2) objective function

(3) constraints

(ii) A company manufactures two products A and B. Production is limited to 80 units and 60 units of products A and B respectively due to limited supply of raw material. Production of product A requires 5 units of electronic components while production of product requires 6 units of electronic components. The electronic components are supplied by another manufacturer and the supply is limited to 600 units per day. The company has 160 employers. The production of one unit of product A requires 1 man-day of labour and one unit of product B requires 2 man-days of labour. Each unit of these products is sold in the market at a profit of Rs 50 and Rs 80 respectively

Formulate the above as a linear programming problem and use a graph paper to determine by graphically how many units of each product the company should produce to maximize profit

(b) (i) Define the following-

(1) basic variables

(2) slack variables

(ii) The manager of a company, which supplies office furniture, has asked to prepare a profit maximizing schedule for the manufacturing of desks, chairs and book-cases. The wooden materials have to be cut properly by machines.
Each unit of desks, chairs and book-cases require 0.8, 0.4 and 0.5 machine hours respectively. The total machine hours available for cutting are 100. The company has 650 man-hours available for painting and polishing. Each unit of desks, chairs and book-cases require 5, 3 and 3 man-hours for painting and polishing. The total capacity of a warehouse where these are to be stored is 1260 square feet. The floor space per unit of desks, chairs and book-cases are 9, 6 and 9 square feet respectively. Each product is supplied is supplied at a profit of $ 30, $ 16 and $ 25 per unit respectively

Determine by Simplex Method the number of units of each product to be manufactured so that the profit is maximum. Interpret your answer